Locally lumped equation of state fluid characterization in reservoir simulation

ABSTRACT

In some embodiments, a method for locally lumped equation of state fluid characterization can include determining a set of components for the material balance calculations for a plurality of grid blocks of a reservoir. The plurality of grid blocks can experience different recovery methods between them. Lumping schemes can be determined for the plurality of grid blocks. Phase behavior calculations can be performed on the plurality of grid blocks, wherein different lumping schemes can be used across the plurality of grid blocks.

BACKGROUND

Equation of State (EOS) fluid characterization can be used to model thebehavior of hydrocarbon reservoir fluids when variation in the fluidcomposition has a significant influence on the recovery of thehydrocarbons. The EOS fluid characterizations can be used as theparameters of PVT equations that relate the pressure, volume andtemperature (PVT) of a system. These equations of state can be used topredict equilibrium conditions such as the number of phases that arepresent in the fluid (e.g., single phase or multiple phases). Theequations can also be used to describe the properties of the phases,such as the density of the phase, and the composition of each phase.

Hydrocarbon fluids may contain thousands of components. It isimpractical to determine the properties of all of these components andto use this number of components in simulation calculations, so EOScharacterizations reduce the number of components by grouping togetherall the components in a range of molecular weights. Each group ofcomponents is referred to as a pseudo-component. The properties of thesepseudo-components are adjusted so that the fluid properties giveacceptable agreement with laboratory data over the range of pressures,temperatures and fluid composition likely to be encountered in thereservoir and the production/injection facilities. For example, for eachpseudo-component of a fluid, the molecular weight, the criticaltemperature, and the critical pressure may all need to be adjusted.Additionally, properties that are used to relate any twopseudo-components (e.g., binary interaction coefficients) may also beadjusted. The cost of calculating fluid properties using an EOScharacterization increases greatly as the number of lumped componentsincreases, so it is advantageous to use the fewest number of lumpedcomponents that can give an acceptable match to the laboratory data.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a reservoir with a different recovery method used ineach of two regions.

FIG. 2 illustrates a table of one embodiment of component lumping.

FIG. 3 illustrates a flowchart of an embodiment of a method for EOSfluid characterization using component lumping.

FIG. 4 illustrates a diagram of an embodiment of a wireline loggingoperation in accordance with various embodiments.

DETAILED DESCRIPTION

During production operations, simulations can be used to model theproperties of fluid reservoirs that may be subjected to differentrecovery mechanisms (e.g. gravity drainage, fluid expansion,displacement by water, gas) A reservoir can be subjected to multipledifferent recovery mechanisms in different geographical locations (e.g.water displacement near an aquifer, gas expansion in a gas cap), and/orfor different periods of time. (e.g., because of the commencement ortermination of gas, water, steam, solvent injection). Each recoverymechanism has a different sensitivity to the composition of thereservoir and injected fluids, and the simulations should take this intoaccount.

The embodiments herein encompass a method that locally lumps a pluralityof components, of the thousands of components that can typically make upa hydrocarbon fluid, to be represented by usually a smaller number ofpseudo-components (i.e., EOS characterization). Components are lumpedtogether to be represented by a pseudo-component having similarproperties as the components being replaced. Unlike the typical methodsof EOS characterization, the embodiments herein provide locally lumpedEOS characterization such that the characterization can vary frompoint-to-point across the reservoir as the recovery mechanisms varyacross the reservoir.

FIG. 1 illustrates a reservoir with a different recovery method used ineach of two regions, and a corresponding different recovery mechanism ineach of these regions. This reservoir is for purposes of illustrationonly as the present embodiments are not limited to any certain quantityof regions nor to any certain recovery mechanism. In other words, thelocally lumped EOS characterization method can adapt to any number andtype of recovery mechanisms across a reservoir, generating a differentgroup of pseudo-components for each different recovery mechanism region.

FIG. 1 shows a gas injection region 101 and a water injection region 102within the same reservoir 100. In other words, in order to recover thehydrocarbon fluid in the reservoir, the water injection region uses awater injection recovery mechanism and the gas injection region uses agas injection recovery mechanism.

Since the water injection recovery mechanism introduces fewer newcomponents than the gas injection recovery mechanism, the waterinjection recovery mechanism can achieve an acceptable accuracy forphase behavior calculations with a fewer number of pseudo-components(NC₁ components) than the gas injection recovery mechanismpseudo-components (NC₂ components). For component mass balancecalculations, the components used in the gas injection recoverymechanism can be used throughout the reservoir 100. However, in thewater injection region 102, these components are first lumped into theNC₁ components for the water injection region 102 and the phase behaviorcalculations can then be performed using the EOS characterization forthe water injection recovery mechanism. The resulting phase compositionscan then be de-lumped and the derivatives of the fluid properties (e.g.,phase densities, saturations, phase compositions) with respect to theNC₁ components can also be de-lumped in order to be expressed withrespect to the original NC₂ components.

The phase behavior calculations with the lumped components can take lessprocessing time than the delumped EOS calculations. This can reduce theprocessing time used for the reservoir simulation. This may beparticularly true if the simulation is run using an Implicit PressureExplicit Saturation (IMPES) formulation, where the component masses aresolved explicitly, rather than an implicit formulation, where thecomponent masses are solved implicitly. The implicit formulation resultsin a much larger system of equations and uses a relatively large amountof processing time to solve the linear system of equations, so the phasebehavior calculations can use a smaller proportion of the totalprocessing time.

The locally lumped EOS characterization method can be used with anylumping scheme. However, the lumped components of FIG. 2 can moreclosely reproduce the solution that would be obtained if the massbalance was performed using the lumped components. The lumped componentscan be chosen so that each of the delumped components makes up a part(or the whole) of only one of the lumped components.

FIG. 2 illustrates a table of one embodiment of component lumping. Thenumber of lumped components and/or their associated delumped componentsare for purposes of illustration only. The quantity of delumpedcomponents represented by each lumped component can vary with eachembodiment. Additionally, the particular delumped components to belumped with a particular lumped component can also vary with eachembodiment.

In this figure, the lumped fluid characterization for the waterinjection recovery mechanism uses six pseudo-components represented byC1 through C6. The lumped fluid characterization used for the gasinjection recovery mechanism uses eleven pseudo-components representedas G1 through G11. For the water injection recovery mechanism,pseudo-component C1 is the same as G1 for the gas injection recoverymechanism, C2 is the sum of G2 and G3, C3 is the sum of G4 and G5, C4 isthe sum of G6 and G7, C5 is the sum of G8 and G9, and C6 is the sum ofG10 and G11. The illustrated choice of lumping has the property that themass balance, using the mass of the components of the secondcharacterization as the primary variables, can give the same result asif the components of the first characterization had been used as theprimary variables.

If the recovery mechanism changes during the simulation, the choice oflumping can be changed to be appropriate for the new recovery mechanism.For example, if part of the reservoir 100 is switched from waterinjection to gas injection, the EOS calculations could be performed witha different set of lumped components and corresponding characterization.

The choice of lumping could also be dynamically chosen based on changesin composition in a grid block. These changes might be a differentrecovery method being used or elements from a recovery method for oneportion of the reservoir invading another portion of the reservoir. Forexample, if the injected gas of FIG. 1 invades the water injectionregion 102, the components in the water injection region 102 willchange. Thus, the choice of lumped components could be switcheddynamically to take into account the additional components in the waterinjection region 102.

However, a change in the lumping and EOS characterization will result inslightly different phase densities and saturations, thus introducing avolume balance error (i.e., the fluid volume no longer exactly equalsthe pore volume in the grid block), This volume balance error willresult in a spurious pressure change in the grid block on the nextiteration of the solution. To avoid this, a onetime adjustment can bemade to the pore volume when the characterization is switched.

FIG. 3 illustrates a flowchart of an embodiment for locally lumped EOSfluid characterization in reservoir simulations. Prior to thesimulation, PVT analysis is performed to develop EOS characterizationsfor each recovery mechanism 301 that will be encountered in thereservoir. Each characterization can have a different number ofpseudo-components, and different properties for any pseudo-componentsthat are in common. The number of components for each characterizationshould be the fewest that are capable of accurately representing thephase behavior for each recovery mechanism. The material balancecomponents used for the material balance calculations are determined bythe characterization with the largest number of components. Thereservoir is divided up into grid blocks, and for each grid block themass of the material balance components is conserved. The materialbalance components for the plurality of grid blocks of the reservoir isdetermined wherein different recovery mechanism are experienced forlocal groupings of grid blocks.

Each grid block is assigned one of the EOS characterizations 303 (e.g.,lumping scheme), depending on the recovery mechanism that is present atthe location of the grid block. If the characterization assigned to agrid block is not the characterization associated with the materialbalance components, then the PVT properties of the fluid in the gridblock (e.g. phase compositions, phase volume, phase density and phaseviscosity) are calculated by first lumping the components into thecomponents associated with the characterization, calculating theproperties using the lumped components, then delumping the phasecompositions and the derivatives of phase volumes, densities andviscosities to get these quantities in terms of the material balancecomponents. The process can be referred to as locally lumped EOS fluidcharacterizations.

In an embodiment, the components from a first recovery mechanism havinga greater number of components can be lumped into the components for asecond recovery mechanism having the least number of components(different from the first recovery mechanism). The reduced number ofcomponents can be referred to as the pseudo-components representing thegreater number of components since they can represent the greater numberof components in phase behavior calculations, thus, reducing theprocessor time used for the reservoir simulation. As seen in FIG. 2 anddiscussed previously, each pseudo-component can represent one or more ofthe material balance components.

Based on the recovery mechanism and/or fluid properties in a particulargrid block or group of grid blocks, phase behavior calculations can beperformed across the reservoir on a grid block or group of grid blocksusing different lumping schemes based on a composition and/or recoverymethod for the grid block or group of grid blocks 305. The resultingphase compositions are delumped 307 and the fluid properties (e.g.,phase densities and saturations, phase compositions) with respect to thelumped components are delumped and expressed with respect to theoriginal delumped components 309. Using this locally lumped EOS fluidcharacterization method, different lumping schemes can be applied todifferent grid blocks and/or at different times (e.g., when the recoverymechanism of a grid block changes).

Data obtained during a wireline sampling operation can be used in thecompositional reservoir simulations. For example, after a recoveryoperation has started on a reservoir, a wireline sampling operation canbe used to obtain a fluid sample that can be used to determine the fluidproperties at a particular location of the reservoir due to componentsbeing added to the reservoir by a particular recovery mechanism. Ifnecessary, the data for the reservoir simulation model can be adjustedto improve the match between the measured fluid properties measured onthe sample, and the fluid properties predicted by using the originalcharacterization at the corresponding grid block in the reservoirsimulation. Adjustments of this kind improve the accuracy of thereservoir simulation, and make it more reliable for predictinghydrocarbon recovery in response to changes in how the reservoir isoperated.

FIG. 4 illustrates generally an example of a wireline sampling system. Ahoist 406 may be included as a portion of a platform 402, such ascoupled to a derrick 404, and used to raise or lower equipment such as awireline sonde 410 into or out of a borehole. In this wireline example,a cable 442 may provide a communicative coupling between a loggingfacility 444 (e.g., including a processor circuit 445 including memoryor other storage or control circuitry) and the sonde 410. In thismanner, information about the reservoir 418 may be obtained. Theprocessor circuit 445 may be configured to execute any methods forcharacterizing fluids, locally lumping a plurality of components, and/orreservoir simulations.

In the foregoing Detailed Description, it can be seen that variousfeatures are grouped together in a single embodiment for the purpose ofstreamlining the disclosure. This method of disclosure is not to beinterpreted as reflecting an intention that the claimed embodimentsrequire more features than are expressly recited in each claim. Rather,as the following claims reflect, inventive subject matter lies in lessthan all features of a single disclosed embodiment. Thus the followingclaims are hereby incorporated into the Detailed Description, with eachclaim standing on its own as a separate embodiment.

1. A method for locally lumped equation of state fluid characterization,the method comprising: determining material balance components for aplurality of grid blocks of a reservoir, wherein different recoverymechanisms are experienced within different groups of grid blocks;determining lumping schemes for the plurality of grid blocks; andperforming phase behavior calculations on the plurality of grid blockswherein different lumping schemes are used across the reservoir.
 2. Themethod of claim 1, wherein determining material balance componentscomprises determining a fluid composition in the plurality of gridblocks by, performing a pressure, volume, temperature analysis of thegrid blocks or groups of grid blocks.
 3. The method of claim 1, furthercomprising delumping phase compositions resulting from the phasebehavior calculations.
 4. The method of claim 3, further comprisingexpressing properties of fluid properties of a grid block or group ofgrid blocks with respect to the material balance components of the gridblock or the group of grid blocks.
 5. The method of claim 1, whereindetermining lumping schemes comprises lumping the material balancecomponents to pseudo-components such that each pseudo-componentrepresents one or more material balance components resulting in areduced quantity of pseudo-components.
 6. The method of claim 5, whereinthe reduced quantity of pseudo-components are less than the quantity ofmaterial balance components.
 7. The method of claim 1, whereinperforming phase behavior calculations on the plurality of grid blockscomprises wherein a first lumping scheme is used for a first grid blockor group of grid blocks at a first time and a second lumping scheme isused for the first grid block or group of grid blocks at a second time.8. The method of claim 7; further comprising changing a recoverymechanism for the first grid block or group of grid blocks between thefirst time and the second time. 9-14. (canceled)
 15. A method forlocally lumped equation of state fluid characterization, the methodcomprising: performing pressure, volume, temperature (PVT)characterizations for each recovery mechanism of a plurality of recoverymechanisms for a reservoir comprising a plurality of grid blocks and aplurality of delumped components; assigning each grid block to a PVTcharacterization; performing phase behavior calculations across thereservoir using different lumping schemes to generate phasecompositions; delumping the phase compositions; and expressing the phasecompositions with respect to the delumped components.
 16. The method ofclaim 15, further comprising dividing the reservoir into a plurality ofgroups of grid blocks, each group of grid blocks experiencing adifferent recovery mechanism.
 17. The method of claim 15, whereinperforming the PVT analysis comprises developing equation of state (EOS)characterizations for each recovery mechanism.
 18. The method of claim15, wherein each PVT characterization comprises a plurality of delumpedcomponents.
 19. The method of claim 15, further comprising determiningmaterial balance components from the PVT characterizations having alargest quantity of delumped components.
 20. The method of claim 19,further comprising conserving the material balance components for eachgrid block.
 21. A system comprising: a processor; and a memory coupledto the processor, the memory storing processor-readable instructions,which, when executed by the processor, cause the processor to perform aplurality of functions, including functions to: perform pressure,volume, temperature (PVT) characterizations for each recovery mechanismof a plurality of recovery mechanisms for a reservoir comprising aplurality of grid blocks and a plurality of delumped components; assigneach grid block to a PVT characterization; perform phase behaviorcalculations across the reservoir using different lumping schemes togenerate phase compositions; delump the phase compositions; and expressthe phase compositions with respect to the delumped components
 22. Thesystem of claim 21, wherein the plurality of functions performed by theprocessor further include functions to divide the reservoir into aplurality of groups of grid blocks, each group of grid blocksexperiencing a different recovery mechanism.
 23. The system of claim 21,wherein the plurality of functions performed by the processor furtherinclude functions to generate equation of state (EOS) characterizationsfor each recovery mechanism.
 24. The system of claim 21, wherein eachPVT characterization comprises a plurality of delumped components. 25.The system of claim 21, wherein the plurality of functions performed bythe processor further include functions to determine material balancecomponents from the PVT characterizations having a largest quantity ofdelumped components.
 26. The system of claim 25, wherein the pluralityof functions performed by the processor further include functions toconserve the material balance components for each grid block.